135L is noticeably lighter than 70-200 L 2.8 non-IS, but both are ok, handheldable to me.
Please keep this in mind : 135L isn't a great option for low light shooting due to the lack of IS and relatively long focal length.
PQ wise 135L is almost perfect.
Another route : get the 100mm f/2 and you might not need to sell the 70-200. The 100mm f/2 weights about 60% of the 135L and 95% of PQ and AF performance. Actually I did that : sold the 135L, got the 70-200 IS II and the 100mm f/2.